docs: Split ui library documentation into guides (#4774)

Split the UI library integration guide into individual how-to guides for
Shadcn/ui, Material-UI, Framer Motion, and Chakra UI.

---

[Open in
Web](https://cursor.com/agents?id=bc-8573175f-c315-4c20-a848-fc2e39ef00eb)
• [Open in
Cursor](https://cursor.com/background-agent?bcId=bc-8573175f-c315-4c20-a848-fc2e39ef00eb)

Learn more about [Background
Agents](https://docs.cursor.com/background-agent/web-and-mobile)

Co-authored-by: Cursor Agent <[email protected]>

Author: tannerlinsley

docs/router/framework/react/how-to/README.md

@@ -14,6 +14,13 @@ This directory contains focused, step-by-step instructions for common TanStack R
 - [Set Up Server-Side Rendering (SSR)](./setup-ssr.md) - Implement SSR with TanStack Router
 - [Migrate from React Router v7](./migrate-from-react-router.md) - Complete migration guide from React Router v7
 
+### UI Library Integration
+
+- [Integrate with Shadcn/ui](./integrate-shadcn-ui.md) - Set up Shadcn/ui components with animations and styling
+- [Integrate with Material-UI (MUI)](./integrate-material-ui.md) - Configure MUI components with proper theming and TypeScript
+- [Integrate with Framer Motion](./integrate-framer-motion.md) - Add smooth animations and transitions to your routes
+- [Integrate with Chakra UI](./integrate-chakra-ui.md) - Build responsive, accessible UIs with Chakra UI components
+
 ## Using These Guides
 
 Each guide follows a consistent structure: